Multiscale Seismology: the future of inversion W. MENKE Lamont-Doherty Earth Observatory Columbia University E. CHESNOKOV and R.L. BROWN Institute for Theoretical Geophysics University of Oklahoma

Thesis The past 15 years has seen a tremendous improvement in the fidelity of many types of seismic images. This improvement was driven by, more and higher quality seismometers, faster computers, better data archiving and processing methodologies. But our ability to integrate knowledge from multiple data types hasn’t kept up. Often different data types are telling us seemingly-contradictory things.

Example: Surface Wave Tomography e.g. of North America

Woodward and Snieder, seismograms

Zhang & Tanimoto, ,000 seismograms globally, about 324 prorated for area

685 seismograms

400,000 seismograms globally, about 7,200 prorated for area note inversion includes transverse anisotropy

“Exponential” growth of data ! Images better & better in evolutionary way

But how do these impressive images connect with other things we know about the earth?

Connection 1 Continental Scale Body Wave Traveltimes

Surface wave models have big asthenospheric LVZ’s that imply very large shadow zones Are such shadows actually observed in continental-scale P or S waves?

Connection 2 SKS Shear Wave Splitting

From Gaherty North America has large amount of transverse anisotropy

Predicts Correctly predicts large Love- Rayleigh discrepancy along paths parallel to MOMA Array

But inconsistent with SKS splitting results along MOMA array Fouch’s splitting data as plotted by Gaherty No plausible anisotropic material can have fast-axis parallel to array and have large Love-Rayleigh discrepancy parallel to the array, too

More overlap in parameters than length scale !

Hypothesis: different length scales strongly influence interpretation

EARTH OBSERVATION INVERSION Strong Spooky Interactions (seismic waves) Length scale of

we understand this interaction pretty well (but only in very idealized media) strong spooky interactions OBSERVATION (seismic waves) EARTH Length scale of

WHAT IS THE STRUCURE OF THIS MEDIUM ? bulk modulus 1 shear modulus 1, density 1 thickness 1 bulk modulus 2 shear modulus 2 density 2 thickness 2

WHAT IS THE STRUCTURE OF THIS MEDIUM ? Inhomogenous with various properties of isotropic layers? YES ! when <<thickness

WHAT IS THE STRUCTURE OF THIS MEDIUM ? Strongly Scattering? YES ! when ~thickness

WHAT IS THE STRUCURE OF THIS MEDIUM ? Effectively homogeneous and anisotropic? YES ! when >>thickness

Theory for understanding this effect in 3-D media with random heterogeneities is well developed … Elasticity and density written in terms of average and deviation from average

Chesnokov et al. 2000Chesnokov weird! effective density is a tensor.. 1. elasticity and density are frequency-dependent 2. integrals embody interaction of wavefield with scale length of heterogeneities … 3. … through correlation functions

“UPSCALING” Example Reconciling Sonic Log with VSP Collect Sonic Logs (500 Hz) of Vp, Vs1, Vs2, density Infer all components of C ijkl (f=500 Hz) Compute Correlation Functions Predict C ijkl (f=50 Hz) Compare with VSP (50 Hz) experiment Is this Inversion? Not quite …

Sonic Log Result for C 55 Predicted VSP VSP

theory can be extended to include more complicated micro- physics e.g. fluid/rock interactions

There’s been some interesting efforts on this side of the triangle, too strong spooky interactions OBSERVATION Length scale of INVERSION Length scale of

True Slip on Hypothetical Fault Three Inversions That Fit the Data Equally Well Results of Slip Inversions Highly Dependent on Scale of Model Representation Courtesy of Morgan Page

A Challenge of the Future Create Earth knowledge that practitioners using different techniques AGREE UPON !

EARTH INVERSION Joint Inversions that handle multiple scales in a Physics-Based way OBSERVATION (seismic waves) Length scale of

The Future ? Scale 1 Data physics-based parameterization 1 Assessment of underlying physics Scale 2 Data Business as Usual Scale 1 Data Ad-hoc parameterization 1 Ad-hoc parameterization 2 Speculative attempts to integrate and reconcile results Scale 2 Data feedback confusion ?! Improved knowledge of earth